optimization problem with 'fminunc' solver for varying size variables?

Hi, All. I have one objective function that I would like to minimize with a large set of variables (well, not that large about 100). I have managed to put all these variables into one vector as x0 for initial condition. The problem is that I am also trying to optimize different partial sets of these variables. Say, I want to optimize 75 parameters while remaining the other 25 as their initial values (as constant) etc.. I have been thinking of create of logic vector like [1 1 0 1 0...] to mask the 25 parameters not involved with the optimization process. But could not realize it yet. Please give some hints, any idea is welcome. Thanks

Answer 1

[Walter Roberson]

Two possible ways:

1) switch to fmincon and for the variables that are to be constants, set their lb and ub to be the same constant

2) construct an anonymous function that takes in a vector of length (e.g.) 75, and creates a new vector of length 100 with the remaining locations filled with the constants. For example,

ReOrder = @(Vector, NewOrder) Vector(NewOrder);
this_objective = @(x) original_objective_function ( ReOrder( [x(:), ConstantParameters(:)], ProperOrder) );

ProperOrder would be a vector indicating for first the (e.g.) 75 parameters and then the (e.g.) 25 constants, where each one goes in the order expected by original_objective_function. For example if you had a logical vector Treat_As_Constant then

ProperOrder = [find(~Treat_As_Constant(:)); find(Treat_As_Constant)];

[Wenwu]

Mr. Walter,

Thanks very much for your quick response with promising solutions. Consider the variable list size, I prefer option 2 of your methods, which is more elegant. I did not try it on my real problem yet, but got challenge with one small trial already:

    original_objective_function = @(x) 100*(x(2)-x(1)^2)^2 + (1-x(1))^2;
    x0 = [-1 2];

    % 1 - varaible not be optimized
    Treat_As_Constant = [1 0];
    ProperOrder = [find(~Treat_As_Constant(:)); find(Treat_As_Constant(:))];

    % define refine anonymous function
    ReOrder = @(Vector, NewOrder) Vector(NewOrder);

    this_objective = @(x) original_objective_function( ReOrder( x(:),  ProperOrder) );
    x_uncon = fminunc(this_objective, x0)

I turns out x_uncon still gets the optimized results for both variable not the one that I planned with one remaining the initial value. Could you tell what's wrong with my implementation? I fell it's the this_objective anonymous function. Thanks

[Walter Roberson]

    original_objective_function = @(x) 100*(x(2)-x(1)^2)^2 + (1-x(1))^2;
    x0 = [-1 2];

    %utility
    ReOrder = @(Vector, NewOrder) Vector(NewOrder);

    % 1 - variable not be optimized
    Treat_As_Constant = logical([1 0]);   %or [true, false]

    [~, ProperOrder] = sort([find(~Treat_As_Constant(:)); find(Treat_As_Constant(:))]);

    % define refine anonymous function
    Constant_Parameters = x0(Treat_As_Constant);
    this_objective = @(x) original_objective_function( ReOrder( [x(:); Constant_Parameters(:)],  ProperOrder) );

    %minimize over non-constant values
    x_uncon = fminunc(this_objective, x0(~Treat_As_Constant));

    %reconstruct pulling constant parameters into place
    x = ReOrder([x_uncon(:), Constant_Parameters(:)], ProperOrder);

[Wenwu]

Mr. Walter,

That works great as planned. Thanks very much for your great explanation as source code.